Common Factors

GCSE(F), GCSE(H),

Factorising an expression involves identifying common factors in the expression, then creating brackets. A common factor can be a number or a letter, or a combination of numbers and letters. It is the opposite of expanding an expression.

An example is to factorise 3x + 9. The number 3 divides into both the 3 (of 3x) and the 9. Create a pair of brackets, and put the common factor outside the brackets, gives:

3x + 9 = 3(x + 3).

Factorising 9ab + 12b has both 3 and b as factors:

9ab + 12b = 3b(3a + 4)

because 3 divides into both 9 and 12, and b divides into both ab and b.

It is often easier to identify one factor at a time: 6x2 - 2x:

6x2 - 2x

= 2(3x2 - x) - identifying 2 as a common factor

= 2x(3x - 1) - identifying x as a common factor.

Examples

1. Factorise 4ab - 20a.

Answer: 4a(b - 5)

The common factors are 4 and a; so the two factors act as multipliers outside the bracket.

2. Factorise 15a2b - 5ab.

Answer: 5ab(3a - 1)

15a2b - 5ab

= 5(3a2b - ab)

= 5a(3ab - b)

= 5ab(3a - 1)

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